The Subatomic World

Soon after the emergence of this ‘planetary’ model of the atom, it was discovered that the number of electrons in the atoms of an element determine the element’s chemical properties, and today we know that the whole periodic table of elements can be built up by successively adding protons and neutrons to the nucleus of the lightest atom-hydrogen*-and the corresponding number of electrons to its atomic ‘shell’.

The interactions between the atoms give rise to the various chemical processes, so that all of chemistry can now in principle be understood on the basis of the laws of atomic physics.

These laws, however, were not easy to recognize.

They were discovered in the 1920s by an international group of physicists including Niels Bohr from Denmark, Louis De Broglie from France, Erwin Schrddinger and Wolfgang Pauli from Austria, Werner Heisenberg from Germany, and Paul Dirac from England.

These men joined their forces across all national borders and shaped one of the most exciting periods in modern science, which brought man, for the first time, into contact with the strange and unexpected reality of the subatomic world.

Every time the physicists asked nature a question in an atomic experiment, nature answered with a paradox, and the more they tried to clarify the situation, the sharper the paradoxes became.

It took them a long time to accept the fact that these paradoxes belong to the intrinsic structure of atomic physics, and to realize that they arise whenever one attempts to describe atomic events in the traditional terms of physics.

Once this was perceived, the physicists began to learn to ask the right questions and to avoid contradictions. In the words of Heisenberg, ‘they somehow got into the spirit of the quantum theory’, and finally they found the precise and consistent mathematical formulation of this theory.

The concepts of quantum theory were not easy to accept even after their mathematical formulation had been completed. Their effect on the physicists’ imaginations was truly shattering.

Rutherford’s experiments had shown that atoms, instead of being hard and indestructible, consisted of vast regions of space in which extremely small particles moved, and now quantum theory made it clear that even these particles were nothing like the solid objects of classical physics.

The subatomic units of matter are very abstract entities which have a dual aspect. Depending on how we look at them, they appear sometimes as particles, sometimes as waves; and this dual nature is also exhibited by light which can take the form of electromagnetic waves or of particles.

This property of matter and of light is very strange. It seems impossible to accept that something can be, at the same time, a particle-i.e. an entity confined to a very small volume-and a wave, which is spread out over a large region of space. This contradiction gave rise to most of the koan-like paradoxes which finally led to the formulation of quantum theory.

The whole development started when Max Planck discovered that the energy of heat radiation is not emitted continuously, but appears in the form of ‘energy packets’. Einstein called these energy packets ‘quanta’ and recognized them as a fundamental aspect of nature. He was bold enough to postulate that light and every other form of electromagnetic radiation can appear not only as electromagnetic waves, but also in the form of these quanta. The light quanta, which gave quantum theory its name, have since been accepted as bona fide particles and are now called photons. They are particles of a special kind, however, massless and always travelling with the speed of light.

The apparent contradiction between the particle and the wave picture was solved in a completely unexpected way which called in question the very foundation of the mechanistic world view-the concept of the reality of matter.

At the subatomic level, matter does not exist with certainty at definite places, but rather shows ‘tendencies to exist’, and atomic events do not occur with certainty at definite times and in definite ways, but rather show ‘tendencies to occur’.

In the formalism of quantum theory, these tendencies are expressed as probabilities and are associated with mathematical quantities which take the form of waves. This is why particles can be waves at the same time. They are not ‘real’ three-dimensional waves like sound or water waves. They are ‘probability waves’, abstract mathematical quantities with all the characteristic properties of waves which are related to the probabilities of finding the particles at particular points in space and at parti- cular times. All the laws of atomic physics are expressed in terms of these probabilities. We can never predict an atomic event with certainty; we can only say how likely it is to happen.

Quantum theory has thus demolished the classical concepts of solid objects and of strictly deterministic laws of nature. At the subatomic level, the solid material objects of classical physics dissolve into wave-like patterns of probabilities, and these patterns, ultimately, do not represent probabilities of things, but rather probabilities of interconnections. A careful analysis of the process of observation in atomic physics has shown that the subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement. Quantum theory thus reveals a basic oneness of the universe. It shows that we cannot decompose the world into independently existing smallest units. As we penetrate into matter, nature does not show us any isolated ‘basic building blocks’, but rather appears as a complicated web of relations between the various parts of the whole. These re- lations always include the observer in an essential way. The human observer constitutes the final link in the chain of ob- servational processes, and the properties of any atomic object can only be understood in terms of the object’s interaction with the observer. This means that the classical ideal of an

objective description of nature is no longer valid. The Cartesian partition between the I and the world, between the observer and the observed, cannot be made when dealing with atomic matter. In atomic physics, we can never speak about nature without, at the same time, speaking about ourselves. The new atomic theory could immediately solve several puzzles which had arisen in connection with the structure of atoms and could not be explained by Rutherford’s planetary model. First of all, Rutherford’s experiments had shown that the atoms making up solid matter consist almost entirely of empty space, as far as the distribution of mass is concerned. But if all the objects around us, and we ourselves, consist mostly of empty space, why can’t we walk through closed doors? In other words, what is it that gives matter its solid aspect?

A second puzzle was the extraordinary mechanical stability of atoms. In the air, for example, atoms collide millions of times every second and yet go back to their original form after each collision. No planetary system following the laws of classical mechanics would ever come out of these collisions unaltered. But an oxygen atom will always retain its characteristic con- figuration of electrons, no matter how often it collides with other atoms. This configuration, furthermore, is exactly the same in all atoms of a given kind. Two iron atoms, and con- sequently two pieces of pure iron, are completely identical, no matter where they come from or how they have been treated in the past.

Quantum theory has shown that all these astonishing pro- perties of atoms arise from the wave nature of their electrons. To begin with, the solid aspect of matter is the consequence of a typical ‘quantum effect’ connected with the dual wave/particle aspect of matter, a feature of the subatomic world which has no macroscopic analogue. Whenever a particle is confined to a small region of space it reacts to this confinement by moving around, and the smaller the region of confinement is, the faster the particle moves around in it. In the atom, now, there are two competing forces. On the one hand, the electrons are bound to the nucleus by electric forces which try to keep them as close as possible. On the other hand, they respond to their confinement by whirling around, and the tighter they are

bound to the nucleus, the higher their velocity will be; in fact, the confinement of electrons in an atom results in enormous velocities of about 600 miles per second! These high velocities make the atom appear as a rigid sphere, just as a fast rotating propeller appears as a disc. It is very difficult to compress atoms any further and thus they give matter its familiar solid aspect.

In the atom, then, the electrons settle in orbits in such a way that there is an optimal balance between the attraction of the nucleus and their reluctance to be confined. The atomic orbits, however, are very different from those of the planets in the solar system, the difference arising from the wave nature of the electrons. An atom cannot be pictured as a small planetary system. Rather than particles circling around the nucleus, we have to imagine probability waves arranged in different orbits. Whenever we make a measurement, we will find the electrons somewhere in these orbits, but we cannot say that they are ‘going around the nucleus’ in the sense of classical mechanics.

In the orbits, the electron waves have to be arranged in such a way that ‘their ends meet’, i.e. that they form patterns known as ‘standing waves’. These patterns appear whenever waves are confined to a finite region, like the waves in a vibrating guitar string, or in the air inside a flute (see diagram overleaf). It is well known from these examples that standing waves can assume only a limited number of well-defined shapes.

In the case of the electron waves inside an atom, this means that they can exist only in certain atomic orbits with definite diameters.

The electron of a hydrogen atom, for example, can only exist in a certain first, second or third orbit, etc., and nowhere in between.

Under normal conditions, it will always be in its lowest orbit, called the ‘ground state’ of the atom.

From there, the electron can jump to higher orbits if it receives the necessary amount of energy. Then the atom is said to be in an ‘excited state’.

It will go back to its ground state after a while, the electron giving off the surplus energy in the form of a quantum of electromagnetic radiation, or photon.

The states of an atom, i.e. the shapes and mutual distances of its electron orbits, are exactly the same for all atoms with the same number of electrons. This is why any two oxygen atoms, for example, will be completely identical. They may be in different excited states, perhaps due to collisions with other atoms in the air, but after a while they will invariably return to exactly the same ground state. The wave nature of the electrons accounts thus for the identity of atoms and for their great mechanical stability.

A further characteristic feature of atomic states is the fact that they can be completely specified by a set of integral numbers, called ‘quantum numbers’, which indicate the loca- tion and shape of the electron orbits. The first quantum number is the number of the orbit and determines the energy an electron must have to be in that orbit; two more numbers specify the detailed shape of the electron wave in the orbit and are related to the speed and orientation of the electron’s rotation.* The fact that these details are expressed by integral numbers means that the electron cannot change its rotation continuously, but can only jump from one value to another, just as it can only jump from one orbit to another. Again the higher values represent excited states of the atom, the ground state being the one where all the electrons are in the lowest possible orbits and have the smallest possible amounts of rotation.

Tendencies to exist, particles reacting to confinement with motion, atoms switching suddenly from one ‘quantum state’ to another, and an essential interconnectedness of all pheno- mena-these are some of the unusual features of the atomic world. The basic force, on the other hand, which gives rise to all atomic phenomena is familiar and can be experienced in the macroscopic world. It is the force of electric attraction between the positively charged atomic nucleus and the negatively charged electrons.

The interplay of this force with the electron waves gives rise to the tremendous variety of structures and phenomena in our environment. It is responsible for all chemical reactions, and for the formation of molecules, that is, of aggregates of several atoms bound to each other by mutual attraction. The interaction between electrons and atomic nuclei is thus the basis of all solids, liquids and gases, and also of all living organisms and of the biological processes associated with them.